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No, they do not. But here are the rules for changing comments to answers and back:

If you promote a comment to an answer, any upvotes on the comment become upvotes on the answer. The answerer's reputation is increased by the value of those upvotes.

If you convert an answer to a comment, any upvotes on the answer become upvotes on the comment. Because upvotes on comments don't affect reputation, the answerer's reputation is reduced by the value of those votes.

If you convert an answer to a comment, any downvotes on the answer are discarded. Any reputation lost because of the downvotes is reversed.

Yes, this does mean that you can eliminate any downvotes on your answer without losing upvotes by converting it to a comment and back. We will not look kindly on anyone caught doing this.

Graeme, I have the impression that this does not work as documented. When comments with votes are promoted to answers, the votes stay there (as wanted), however in my experience the reputation remains unchanged. - No big deal, but I just wanted to let you know...

You are correct. When an answer is converted to a comment, the reputation was adjusted, but not the other way. This should be fixed now. Note that reputation is not adjusted retroactively so this will only affect comments changed to answers in the future.